Details

sample512.0ms

Algorithm

intervals

Results

55.0ms	39×	body	1280	valid
36.0ms	295×	body	80	nan
19.0ms	151×	body	80	valid
18.0ms	28×	body	1280	nan
17.0ms	32×	body	640	valid
8.0ms	18×	body	640	nan
8.0ms	21×	body	320	valid
4.0ms	13×	body	160	valid
3.0ms	7×	body	320	nan
1.0ms	6×	body	160	nan

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	2276
6	1138
5	616
4	361
3	179
2	90
1	39
0	18

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
14.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.8b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

58.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
13.0ms	(* (sqrt 2.0) t)
23.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
54.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

628.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
84.0ms	(* (sqrt 2.0) t)
372.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1572
1	445
0	167

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.5b

localize52.0ms

Local error

Found 4 expressions with local error:

4.4b	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
5.9b	(/ (* l l) x)
8.8b	(/ (* t t) x)
28.5b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-*r/`
6×	`associate-/r*` `times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`associate-+r+` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 74

Calls

4 calls:

28.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
8.0ms	(/ (* l l) x)
7.0ms	(/ (* t t) x)
33.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
22.0ms	(/ (* l l) x)
26.0ms	(/ (* t t) x)
204.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

simplify1.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5012
2	2531
1	547
0	167

prune662.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize65.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* l (/ l x)) (* t t))
4.4b	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t))))
8.8b	(/ (* t t) x)
28.5b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `associate-*r/` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+r+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 64

Calls

4 calls:

16.0ms	(+ (* l (/ l x)) (* t t))
18.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t))))
8.0ms	(/ (* t t) x)
35.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t)))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* l (/ l x)) (* t t))
94.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t))))
37.0ms	(/ (* t t) x)
221.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t)))))

simplify1.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5004
2	2151
1	475
0	150

prune652.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.3b

localize83.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
4.4b	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
8.8b	(/ (* t t) x)
28.5b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `associate-*r/` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+r+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 64

Calls

4 calls:

46.0ms	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
20.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
8.0ms	(/ (* t t) x)
35.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
105.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
28.0ms	(/ (* t t) x)
243.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

simplify1.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	2238
1	482
0	151

prune583.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

regimes962.0ms

Accuracy

77.7% (5.2b remaining)

Error of 9.0b against oracle of 3.7b and baseline of 27.3b

bsearch241.0ms

Steps

Iters	Range		Point
3	4.1523530552241535e+92	5.424691173039659e+92	4.225315466536892e+92
7	-1.3589006648119579e+99	-3.650405087160364e+97	-6.758930516841978e+97

simplify25.0ms

Iterations

Iter	Nodes
done	53
1	53
0	41

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.6s	9914×	body	80	nan
660.0ms	870×	body	1280	valid
603.0ms	1037×	body	640	valid
581.0ms	5072×	body	80	valid
463.0ms	347×	body	160	valid
406.0ms	633×	body	1280	nan
334.0ms	580×	body	640	nan
195.0ms	674×	body	320	valid
150.0ms	341×	body	320	nan
35.0ms	194×	body	160	nan